There are many rhetorical and literary devices in King's "I Have a Dream" speech, and I will focus on three or four that I believe have a dramatic impact on King's audience.
First, King begins the speech with
Five score years ago, a great American, in whose symbolic shadow we stand, signed the Emancipation Proclamation.
This is a masterful way to begin a speech on civil rights because King is using the same phrasing that Abraham Lincoln used for the beginning of the Gettysburg Address in 1863, and that allusion would have resonated with every listener on the Washington Mall in 1963. King links the two events in that one phrase--the dedication of the cemetery for one of the costliest battles of the Civil War and the African-American struggle for civil rights.
King uses metaphorical language extraordinarily well throughout the speech. For example, he compares the Declaration of Independence to a "promissory note to which every American was to fall heir. This note was a promise that all men would be guaranteed the inalienable rights of life, liberty, and the pursuit of happiness." Most of his audience that day (and afterward) would immediately understand the comparison between the Declaration and a promissory note because most Americans by then had signed a promissory note, a promise to pay, in order to purchase a car, a home, a refrigerator. King is very effectively reminding the audience that the promise to pay with freedom has not yet been accomplished.
Because King is making a speech, rather than writing something to be read at leisure, his choice of vocabulary to make his points is critical. As is typical in King's writing or speeches, every time he discusses an abstract concept like racial injustice or hate or justice, he uses descriptive, concrete language to create an image in his listener's mind:
This is no time to engage in the luxury of cooling off or to take the tranquilizing drug of gradualism. Now is the time to rise from the dark and desolate valley of segregation to the sunlit path of racial justice.
As you can see, the abstractions of gradualism, that is, taking too much time to achieve civil rights, and segregation are made real by using language that actually creates an image--"tranquilizing drug" and "desolate valley." It is almost impossible to find an abstract concept in King's speech that is not turned into a specific, concrete image so that the audience can "see" King's ideas not merely hear them.
When King gets to what is called the peroration of the speech, the climax, he uses anaphora, the repetition of key words, to emphasize his argument. In this case, he introduces a series of hopes with the words "I have a dream," which he repeats nine times to reinforce in the minds of his audience that he is still, unfortunately, talking about a dream rather than a reality.
I've discussed only a few of several skillful uses of language and rhetorical techniques. King, as a minister schooled in the art of giving sermons, well understood the power of language and rhetoric to draw his audience into his world, and this speech is perhaps the best example of those skills in action.